Does Psalm 114 commemorate the Passover?

The Passover is a meal that was eaten by the Israelite slaves in Egypt on the evening when the Angel of Death passed through and killed the firstborn people and even animals of Egypt.  Except not the Israelites or their animals.  If the Israelites had marked their door with the blood of a slain innocent lamb that they had eaten that evening, then the Angel of Death 'passed over' their household as it went about its assignment of slaying the firstborn. 

  Here, from Bible Gateway, is how Exodus chapter 12 reads:

12 The Lord said to Moses and Aaron in Egypt, ² “This month is to be for you the first month, the first month of your year. ³ Tell the whole community of Israel that on the tenth day of this month each man is to take a lamb^[a] for his family, one for each household. ⁴ If any household is too small for a whole lamb, they must share one with their nearest neighbor, having taken into account the number of people there are. You are to determine the amount of lamb needed in accordance with what each person will eat. ⁵ The animals you choose must be year-old males without defect, and you may take them from the sheep or the goats. ⁶ Take care of them until the fourteenth day of the month, when all the members of the community of Israel must slaughter them at twilight. ⁷ Then they are to take some of the blood and put it on the sides and tops of the doorframes of the houses where they eat the lambs. ⁸ That same night they are to eat the meat roasted over the fire, along with bitter herbs, and bread made without yeast. ⁹ Do not eat the meat raw or boiled in water, but roast it over a fire—with the head, legs and internal organs. ¹⁰ Do not leave any of it till morning; if some is left till morning, you must burn it. ¹¹ This is how you are to eat it: with your cloak tucked into your belt, your sandals on your feet and your staff in your hand. Eat it in haste; it is the Lord’s Passover.

¹² “On that same night I will pass through Egypt and strike down every firstborn of both people and animals, and I will bring judgment on all the gods of Egypt. I am the Lord. ¹³ The blood will be a sign for you on the houses where you are, and when I see the blood, I will pass over you. No destructive plague will touch you when I strike Egypt.

¹⁴ “This is a day you are to commemorate; for the generations to come you shall celebrate it as a festival to the Lord—a lasting ordinance. ¹⁵ For seven days you are to eat bread made without yeast. On the first day remove the yeast from your houses, for whoever eats anything with yeast in it from the first day through the seventh must be cut off from Israel. ¹⁶ On the first day hold a sacred assembly, and another one on the seventh day. Do no work at all on these days, except to prepare food for everyone to eat; that is all you may do.

¹⁷ “Celebrate the Festival of Unleavened Bread, because it was on this very day that I brought your divisions out of Egypt. Celebrate this day as a lasting ordinance for the generations to come. ¹⁸ In the first month you are to eat bread made without yeast, from the evening of the fourteenth day until the evening of the twenty-first day. ¹⁹ For seven days no yeast is to be found in your houses. And anyone, whether foreigner or native-born, who eats anything with yeast in it must be cut off from the community of Israel. ²⁰ Eat nothing made with yeast. Wherever you live, you must eat unleavened bread.”

²¹ Then Moses summoned all the elders of Israel and said to them, “Go at once and select the animals for your families and slaughter the Passover lamb. ²² Take a bunch of hyssop, dip it into the blood in the basin and put some of the blood on the top and on both sides of the doorframe. None of you shall go out of the door of your house until morning. ²³ When the Lord goes through the land to strike down the Egyptians, he will see the blood on the top and sides of the doorframe and will pass over that doorway, and he will not permit the destroyer to enter your houses and strike you down.

²⁴ “Obey these instructions as a lasting ordinance for you and your descendants. ²⁵ When you enter the land that the Lord will give you as he promised, observe this ceremony. ²⁶ And when your children ask you, ‘What does this ceremony mean to you?’ ²⁷ then tell them, ‘It is the Passover sacrifice to the Lord, who passed over the houses of the Israelites in Egypt and spared our homes when he struck down the Egyptians.’” Then the people bowed down and worshiped. ²⁸ The Israelites did just what the Lord commanded Moses and Aaron.

²⁹ At midnight the Lord struck down all the firstborn in Egypt, from the firstborn of Pharaoh, who sat on the throne, to the firstborn of the prisoner, who was in the dungeon, and the firstborn of all the livestock as well. ³⁰ Pharaoh and all his officials and all the Egyptians got up during the night, and there was loud wailing in Egypt, for there was not a house without someone dead.

 End Quote

  If you noticed, this was done on the newly assigned calendar, a calendar assigned by God Himself, on the 1st month, on the 14th day.  Month 1.  Day 14.  1,14  It was a marvelous deliverance of the captive people of Israel from their captors.  The next day the Israelites fled Egypt.  Essentially that day was the birth of Israel as a nation.  Forty years later they began to conquer the Holy Land. 

  So, since it was on this Month 1, Day 14 that the Passover occurred, is it a coincidence that the Psalm denoted by those same numbers, Psalm 114, speaks of these exact same events that began at the Passover:  the liberation of Israel from its captors, the Egyptians?

Psalm 114